BIT Numerical Mathematics

, Volume 56, Issue 2, pp 633–657 | Cite as

Analysis and numerical solution of linear delay differential-algebraic equations

  • Phi Ha
  • Volker MehrmannEmail author


The analysis and numerical solution of initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Characteristic properties of DDAEs are analyzed and the differences between causal and noncausal DDAEs are studied. The method of steps is analyzed and it is shown that it has to be modified for general DDAEs. The classification of ordinary delay differential equations is generalized to DDAEs, and a numerical solution procedure for general retarded and neutral DDAEs is constructed. The properties of the algorithm are studied and the theoretical results are illustrated with a numerical example.


Delay differential-algebraic equation Differential-algebraic equation Delay differential equations  Method of steps Derivative array Classification of DDAEs 

Mathematics Subject Classification

34A09 34A12 65L05 65H10 



This work was supported by DFG Collaborative Research Centre 910, Control of self-organizing nonlinear systems: Theoretical methods and concepts of application. We thank Ma Vinh Tho for support in the numerical tests.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Institut für Mathematik, MA 4-5, TU BerlinBerlinGermany
  2. 2.Department of MathematicsHumboldt University of BerlinBerlinGermany

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